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Maximal Subsemigroups of Finite Transformation Semigroups K(n,r) 被引量：19

Maximal Subsemigroups of Finite Transformation Semigroups K(n,r)
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摘要 Let T n be the full transformation semigroup on the n-element set X n . For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α ∈? T n : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of T n . Let T n be the full transformation semigroup on the n-element set X n . For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α ∈? T n : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of T n .
作者 HaoBoYANG XiuLiangYANG
机构地区 DepartmentofMathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第3期475-482,共8页 数学学报（英文版）
基金 supported by N.S.F.of Zhejiang Province and Hangzhou Teachers College
关键词 Transformation semigroup Maximal subsemigroups Transformation semigroup Maximal subsemigroups
分类号 O152 [理学—基础数学]
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参考文献11

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同被引文献60

  • 1张传军,林屏峰,马敏耀.有限保序变换半群O_n的极大子半群[J].贵州师范大学学报（自然科学版）,2006,24(4):82-85. 被引量：2
  • 2You T, Yang X. A classification of the maximal idempo- tent - generated subsemigroups of finite singular semig- roups [ J ]. Semigroup Forum,2002,64 (2) : 236 - 242.
  • 3Yang X, Yang H. Maximal regular subsemibands of Sing, [J]. Semigroup Forum,2006,72( 1 ) :75 -93.
  • 4Ping Zhao. A classification of maximal idempotent - gen- erated subsemigroups of singular orientation - preserving transformation semigroups [ J ]. Semigroup Forum, 2009, 79(2) :377 -384.
  • 5I. Dimimtrova, J. Koppitz. On the maximal regular sub- semigroups of ideals of order - preserving or order - re- versing transformations [ J ]. Semigroup Forum, 2011,82 (1) :172 -180.
  • 6I. Dimitrova and J. Koppitz. On the monoid of all partial order - preserving extensive transformations [ J ]. Comm. Algebra,2012,40(5 ) : 1821 - 1826.
  • 7Ping Zhao, Huabi Hu and Taijie You. A note on maximal regular subsemigroups of transformation semigroups [ J ]. Semigroup Forum ,2014,88(2) :324 - 334.
  • 8HOWIE J M. Fundamentals of semigroup theory[ M]. Ox- ford :The Clarendon Press, 1995 : 1 - 349.
  • 9Umar A. On the ranks of certain finite semigroups of or- der - decreasing transformations [ J ]. Portugaliae Mathe- matica, 1996,53 ( 1 ) :23 - 34.
  • 10YANG Xiuliang.Maximal Subsemigroups of the Finite Singular Transformation Semigroup[J].Communications in Algebra,2001,29(3):1175-1182.

引证文献19

二级引证文献23

Acta Mathematica Sinica,English Series
2004年 第3期

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